The Raiser's Edge does not send a notification to the donor if the card is declined.  Someone at the organization will need to contact the donor.   The donor should then contact the card-issuing bank to determine the reason for the decline.

If using IATS, you can access your journal report and run a cc reject report for a given day, which tells you which cards were rejected and why. If unsure how to run this report, contact IATS for assistance.

If using PayPal, you may contact PayPal and ask them to run a Declined Cards Report to obtain this information.